The spectrum of natural oscillations of an array of micro- or nanospheres on an elastic substrate

The mechanical properties and structure of spherical nanoparticles in relationship to their natural oscillations were studied. Several first eigenfrequencies of nanodimensional spherical particles could be determined from an analysis of the spectrum of natural oscillations of a substrate bearing an array of attached nanoparticles. A numerical analysis of the natural oscillations of the substrate covered with attached microspheres was performed using the finite element method. The oscillation modes were analyzed for systems with various numbers of nanoparticles, different geometries, and different types of substrate supporting. Results show the localization of natural oscillations in the nanoparticles at frequencies corresponding to the first several eigenmodes of the attached shell.